Will my Blender installation work after updating to windows 10?
You can save your files in a save place, uninstall blender, update to windows 10, and install the last version of blender (2.77a when writing this) so you have a clean version.

As you can see in blender.org the last version is "Compatible with Windows 10 | 8 | 7 | Vista" so you won't have any* problem.

Or at least not more problems than with windows 7.